Genus two nilpotent graphs of finite commutative rings

DOI10.1142/s0219498823501232zbMath1521.05217OpenAlexW4221088413MaRDI QIDQ6161871

P. Vignesh, T. Tamizh Chelvam, G. Kalaimurugan

Publication date: 28 June 2023

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219498823501232

zbMATH Keywords

genuscommutative ringzerodivisor graphessential graphnilpotent graph

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Structure of finite commutative rings (13M05) Combinatorial aspects of commutative algebra (05E40) General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.) (13A70)

Cites Work

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• Classification of non-local rings with genus two zero-divisor graphs
• On zero-divisor graphs of small finite commutative rings
• Correction to: ``Classification of non-local rings with genus two zero-divisor graphs
• Nilpotent graphs of genus one
• Local Rings with Genus Two Zero Divisor Graph
• Exchange Rings Satisfying the n-Stable Range Condition, II
• Finite commutative ring with genus two essential graph
• On the Genus of the Total Graph of a Commutative Ring
• Graphs from Rings
• On the essential graph of a commutative ring

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